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  <doc>
    <id>735</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2003-05-12</completedDate>
    <publishedDate>2003-05-12</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Asymptotic Mesh Independence of Newton's Method Revisited</title>
    <abstract language="eng">The paper presents a new affine invariant theory on asymptotic mesh independence of Newton's method in nonlinear PDEs. Compared to earlier attempts, the new approach is both much simpler and more natural from the algorithmic point of view. The theory is exemplified at collocation methods for ODE boundary value problems and at finite element methods for elliptic PDE problems.</abstract>
    <identifier type="serial">03-13</identifier>
    <identifier type="opus3-id">736</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-7352</identifier>
    <enrichment key="SourceTitle">Appeared in: SIAM Journal on Numerical Analysis Vol. 42, No. 5, pp. 1830-1845</enrichment>
    <author>Martin Weiser</author>
    <author>Anton Schiela</author>
    <author>Peter Deuflhard</author>
    <series>
      <title>ZIB-Report</title>
      <number>03-13</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>mesh independence</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>nonlinear partial differential equations</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Newton method</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>finite element method</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>collocation method</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="65J15">Equations with nonlinear operators (do not use 65Hxx)</collection>
    <collection role="msc" number="65N22">Solution of discretized equations [See also 65Fxx, 65Hxx]</collection>
    <collection role="msc" number="65N30">Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="persons" number="deuflhard">Deuflhard, Peter</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/735/ZR-03-13.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/735/ZR-03-13.pdf</file>
  </doc>
  <doc>
    <id>766</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2003-12-09</completedDate>
    <publishedDate>2003-12-09</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A new Finite Element realization of the Perfectly Matched Layer Method for Helmholtz scattering problems on polygonal&#13;
domains in 2D</title>
    <abstract language="eng">In this paper we propose a new finite element realization of the Perfectly Matched Layer method (PML-method). Our approach allows to deal with arbitrary shaped polygonal domains and with certain types of inhomogeneous exterior domains. Among the covered inhomogeneities are open waveguide structures playing an essential role in integrated optics. We give a detailed insight to implementation aspects. Numerical examples show exponential convergence behavior to the exact solution with the thickness of the PML sponge layer.</abstract>
    <identifier type="serial">03-44</identifier>
    <identifier type="opus3-id">767</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-7662</identifier>
    <identifier type="doi">10.1016/j.cam.2005.03.047</identifier>
    <enrichment key="SourceTitle">Appeared in: Journal of computational and applied mathematics, 188(2006)12-32</enrichment>
    <author>Lin Zschiedrich</author>
    <author>Roland Klose</author>
    <author>Achim Schädle</author>
    <author>Frank Schmidt</author>
    <series>
      <title>ZIB-Report</title>
      <number>03-44</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>transparent boundary conditions</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>perfectly matched layer</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>pole condition</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="35Q60">PDEs in connection with optics and electromagnetic theory</collection>
    <collection role="msc" number="65-04">Explicit machine computation and programs (not the theory of computation or programming)</collection>
    <collection role="msc" number="65N30">Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="institutes" number="compnano">Computational Nano Optics</collection>
    <collection role="persons" number="zschiedrich">Zschiedrich, Lin Werner</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/766/ZR-03-44.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/766/ZR-03-44.pdf</file>
  </doc>
  <doc>
    <id>395</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>1999-03-09</completedDate>
    <publishedDate>1999-03-09</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A Subspace Cascadic Multigrid Method for Mortar Elements</title>
    <abstract language="eng">A cascadic multigrid (CMG) method for elliptic problems with strong material jumps is proposed and analyzed. Non--matching grids at interfaces between subdomains are allowed and treated by mortar elements. The arising saddle point problems are solved by a subspace confined conjugate gradient method as smoother for the CMG. Details of algorithmic realization including adaptivity are elaborated. Numerical results illustrate the efficiency of this CMG algorithm.</abstract>
    <identifier type="serial">SC-99-07</identifier>
    <identifier type="opus3-id">396</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-3954</identifier>
    <enrichment key="SourceTitle">Appeared in: Computing 69 (2002) 205-225</enrichment>
    <author>Dietrich Braess</author>
    <author>Peter Deuflhard</author>
    <author>Konstantin Lipnikov</author>
    <series>
      <title>ZIB-Report</title>
      <number>SC-99-07</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Finite Elements</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Rayleigh-Ritz and Galerkin Methods</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Multigrid Methods</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Domain Decomposition</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="65N30">Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods</collection>
    <collection role="msc" number="65N55">Multigrid methods; domain decomposition</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="persons" number="deuflhard">Deuflhard, Peter</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/395/SC-99-07.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/395/SC-99-07.pdf</file>
  </doc>
  <doc>
    <id>422</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>1999-09-21</completedDate>
    <publishedDate>1999-09-21</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Differential Equations in Technology and Medicine. Computational Concepts, Adaptive Algorithms, and Virtual
Labs</title>
    <abstract language="eng">This series of lectures has been given to a class of mathematics postdocs at a European summer school on Computational Mathematics Driven by Industrial Applications in Martina Franca, Italy (organized by CIME). It deals with a variety of challenging real life problems selected from clinical cancer therapy, communication technology, polymer production, and pharmaceutical drug design. All of these problems from rather diverse application areas share two common features: (a) they have been modelled by various differential equations -- elliptic, parabolic, or Schrödinger--type partial differential equations, countable ordinary diffential equations, or Hamiltonian systems, (b) their numerical solution has turned out to be real challenge to computational mathematics.</abstract>
    <identifier type="serial">SC-99-34</identifier>
    <identifier type="opus3-id">423</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-4223</identifier>
    <enrichment key="SourceTitle">Appeared in: Computational Mathematics Driven by Industrial Problems. Springer 2000. Lecture Notes in Mathematics, 1739, pp. 69-125</enrichment>
    <author>Peter Deuflhard</author>
    <series>
      <title>ZIB-Report</title>
      <number>SC-99-34</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>differential equations:</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>ordinary</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>partial</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>countable</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>hamiltonian</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>finite element methods:</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>adaptive</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>multilevel</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>grid generation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>medical t</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="65-02">Research exposition (monographs, survey articles)</collection>
    <collection role="msc" number="65C05">Monte Carlo methods</collection>
    <collection role="msc" number="65C20">Models, numerical methods [See also 68U20]</collection>
    <collection role="msc" number="65F15">Eigenvalues, eigenvectors</collection>
    <collection role="msc" number="65J10">Equations with linear operators (do not use 65Fxx)</collection>
    <collection role="msc" number="65L05">Initial value problems</collection>
    <collection role="msc" number="65L08">Improperly posed problems</collection>
    <collection role="msc" number="65N25">Eigenvalue problems</collection>
    <collection role="msc" number="65N30">Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods</collection>
    <collection role="msc" number="65N55">Multigrid methods; domain decomposition</collection>
    <collection role="msc" number="78A50">Antennas, wave-guides</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="persons" number="deuflhard">Deuflhard, Peter</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/422/SC-99-34.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/422/SC-99-34.pdf</file>
  </doc>
  <doc>
    <id>429</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>1999-12-06</completedDate>
    <publishedDate>1999-12-06</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Algebraic Multigrid by Component Splitting for Edge Elements on Simplicial Triangulations</title>
    <abstract language="eng">Our focus is on Maxwell's equations in the low frequency range; two specific applications we aim at are time-stepping schemes for eddy current computations and the stationary double-curl equation for time-harmonic fields. We assume that the computational domain is discretized by triangles or tetrahedrons; for the finite element approximation we choose N\'{e}d\'{e}lec's $H(curl)$-conforming edge elements of the lowest order. For the solution of the arising linear equation systems we devise an algebraic multigrid preconditioner based on a spatial component splitting of the field. Mesh coarsening takes place in an auxiliary subspace, which is constructed with the aid of a nodal vector basis. Within this subspace coarse grids are created by exploiting the matrix graphs. Additionally, we have to cope with the kernel of the $curl$-operator, which comprises a considerable part of the spectral modes on the grid. Fortunately, the kernel modes are accessible via a discrete Helmholtz decomposition of the fields; they are smoothed by additional algebraic multigrid cycles. Numerical experiments are included in order to assess the efficacy of the proposed algorithms.</abstract>
    <identifier type="serial">SC-99-40</identifier>
    <identifier type="opus3-id">429</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-4290</identifier>
    <author>Rudolf Beck</author>
    <series>
      <title>ZIB-Report</title>
      <number>SC-99-40</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Algebraic multigrid</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>mesh coarsening</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>edge elements</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>N\'{e}d\'{e}lec spaces</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Maxwell's equations</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="35Q60">PDEs in connection with optics and electromagnetic theory</collection>
    <collection role="msc" number="65-XX">NUMERICAL ANALYSIS</collection>
    <collection role="msc" number="65F10">Iterative methods for linear systems [See also 65N22]</collection>
    <collection role="msc" number="65N30">Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods</collection>
    <collection role="msc" number="65N55">Multigrid methods; domain decomposition</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/429/SC-99-40.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/429/SC-99-40.pdf</file>
  </doc>
  <doc>
    <id>622</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2000-12-19</completedDate>
    <publishedDate>2000-12-19</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Adaptive Multigrid Methods for the Vectorial Maxwell Eigenvalue Problem for Optical Waveguide Design</title>
    <abstract language="eng">This paper has been motivated by the need for a fast robust adaptive multigrid method to solve the vectorial Maxwell eigenvalue problem arising from the design of optical chips. Our nonlinear multigrid methods are based on a previous method for the scalar Helmholtz equation, which must be modified to cope with the null space of the Maxwell operator due to the divergence condition. We present two different approaches. First, we present a multigrid algorithm based on an edge element discretization of time-harmonic Maxwell's equations, including the divergence condition. Second, an explicit elimination of longitudinal magnetic components leads to a nodal discretization known to avoid discrete \emph{spurious modes} also and a vectorial eigenvalue problem, for which we present a multigrid solver. Numerical examples show that the edge element discretization clearly outperforms the nodal element approach.</abstract>
    <identifier type="serial">00-54</identifier>
    <identifier type="opus3-id">623</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-6228</identifier>
    <enrichment key="SourceTitle">Appeared in: W. Jäger et al. (eds.) Mathematics - Key Technology for the Future : Joint Projects between Universities and Industry. Springer 2003. Pp. 279 -292</enrichment>
    <author>Frank Schmidt</author>
    <author>Tilmann Friese</author>
    <author>Lin Zschiedrich</author>
    <author>Peter Deuflhard</author>
    <series>
      <title>ZIB-Report</title>
      <number>00-54</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Maxwell's equations</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>eigenvalue problem</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>edge elements</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>multigrid methods</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>waveguide</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>optical chip design</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="65N25">Eigenvalue problems</collection>
    <collection role="msc" number="65N30">Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods</collection>
    <collection role="msc" number="65N55">Multigrid methods; domain decomposition</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="persons" number="deuflhard">Deuflhard, Peter</collection>
    <collection role="persons" number="zschiedrich">Zschiedrich, Lin Werner</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/622/ZR-00-54.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/622/ZR-00-54.pdf</file>
  </doc>
  <doc>
    <id>596</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2000-08-30</completedDate>
    <publishedDate>2000-08-30</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Electromagnetic phased arrays for regional hyperthermia -- optimal frequency and antenna arrangement</title>
    <abstract language="eng">In this paper we investigate the effects of the three-dimensional arrangement of antennas and frequency on temperature distributions that can be achieved in regional hyperthermia using an electromagnetic phased array. We compare the results of power-based and temperature-based optimization. Thus we are able to explain the discrepancies between previous studies favouring more antenna rings on the one hand and more antennas per ring on the other hand. We analyze the sensitivity of the results with respect to changes in amplitudes and phases as well as patient position. This analysis can be used for different purposes. First, it provides additional criteria for selecting the optimal frequency. Second, it can be used for specifying the required phase and amplitude accuracy for a real phased array system. Furthermore, it may serve as a basis for technological developments in order to reduce both types of sensitivities described above.</abstract>
    <identifier type="serial">00-28</identifier>
    <identifier type="opus3-id">597</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-5961</identifier>
    <enrichment key="SourceTitle">Appeared in: International Journal of Hyperthermia 17 (4), 2001, pp. 321-336</enrichment>
    <author>Martin Seebass</author>
    <author>Rudolf Beck</author>
    <author>Johanna Gellermann</author>
    <author>Jacek Nadobny</author>
    <author>Peter Wust</author>
    <series>
      <title>ZIB-Report</title>
      <number>00-28</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Pelvic heating</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>phased array optimization</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="65N30">Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods</collection>
    <collection role="msc" number="92C50">Medical applications (general)</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/596/ZR-00-28.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/596/ZR-00-28.pdf</file>
  </doc>
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